2022/11/29 by Merlin Humml, Humml, Merlin, Lutz Schröder +1
Computer Science · #03B42 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.AI #cs.LO #msc:03B42
paper · pdf · doi:10.48550/arxiv.2211.16284
Version with appendix of the AAAI23 publication
arxiv created 2022/11/29 · arxiv updated 2022/11/30
Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge among economists'. We introduce such a logic of common knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic that we keep generic, with one possible agent logic being ALC. We show that AGEL is EXPTIME-complete, with the lower bound established by reduction from standard group epistemic logic, and the upper bound by a satisfiability-preserving embedding into the full μ-calculus. Further main results include a finite model property (not enjoyed by the full μ-calculus) and a complete axiomatization.